Non-Newtonian rheology property for two-phase flow on fingering phenomenon in porous media using the lattice Boltzmann method

Fingering phenomenon takes place when a less viscous fluid displaces a more viscous fluid and it has been extensively studied due to the importance in industrial fields. In this paper, a lattice Boltzmann method for immiscible non-Newtonian two-phase flow is proposed. The fundamental physical mechanisms of Newtonian fluid displacing non-Newtonian fluid in porous media are investigated in terms of power-law exponent, capillary number, viscosity ratio, surface wettability, Bond number and geometry. The numerical results provide a good understanding of the mechanism for Newtonian fluid displacing non-Newtonian fluid from a mesoscopic point of view, and it also demonstrates that the lattice Boltzmann method is a useful tool for simulating non-Newtonian two-phase flow in porous media.